Construction of one-gray weight codes and two-Gray weight codes over ℤ<Subscript>4</Subscript> + <Emphasis Type="Italic">u</Emphasis>ℤ<Subscript>4</Subscript>

This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over ?₄+u?₄(u ² = u) with type \({16^{{k_1}}}{8^{{k_2}}}{8^{{k_3}}}{4^{{k_4}}}{4^{{k_5}}}{4^{{k_6}}}{2^{{k_7}}}{2^{{k_8}}}\) based on a distance-preserving Gray map from (?₄ + u?₄) ⁿ to ? ₄ ²ⁿ . Secondly, the authors use the similar approach to do works on two-Gray (projective) weight linear codes. Finally, some examples are given to illustrate the construction methods.     

Construction of One-Lee Weight and Two-Lee Weight Codes over IF_p+vIF_p

This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over IF_p+vIF_p(v~2=v) with type p~(2 k_1)p~(k2)p~(k3) based on two different distance-preserving Gray maps from((IF_p+vIF_p)~n, Lee weight) to(IF_p~(2 n), Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p=2.     

On the Gray Images of Some Constacyclic Codes over F_p+uF_p+u~2F_p

Constacyclic codes are an important class of linear codes in coding theory.Many optimal linear codes are directly derived from constacyclic codes.In this paper,a new Gray map between codes over F_p+uF_p+u~2F_p and codes over Fp is defined,where p is an odd prime.By means of this map,it is shown that the Gray image of a linear(1+u+u~2)-constacyclic code over F_p+uF_p+u~2F_p of length n is a repeated-root cyclic code over F_p of length pn.Furthermore,some examples of optimal linear cyclic codes over F_3 from(1+u+u~2)-constacyclic codes over F_3+uF_3+u~2F_3 are given.     

Macwilliams Identities of Linear Codes over the Ring F_2+ uF_2+ vF_2

The Lee weight enumerators and the complete weight enumerators for the linear codes over ring R = F2 + u F2 + v F2 are defined and Gray map from Rnto F3n2 is constructed. By proving the fact that the Gray images of the self-dual codes over R are the self-dual codes over F2, and based on the Mac Williams identities for the Hamming weight enumerators of linear codes over F2, the Mac Williams identities for Lee weight enumerators of linear codes over R are given. Further, by introducing a special variable t, the Mac Williams identities for the complete weight enumerators of linear codes over R are obtained. Finally, an example which illustrates the correctness and function of the two Mac Williams identities is provided.     

Optimal p-Ary Codes from One-Weight and Two-Weight Codes over IF_p+ vIF_p

This paper is devoted to determining the structures and properties of one-Lee weight codes and two-Lee weight projective codes Ck1,k2,k3 over p IF+ v IFp with type p2k1pk2pk3. The authors introduce a distance-preserving Gray map from( IFp + v IFp)nto2np. By the Gray map, the authors construct a family of optimal one-Hamming weight p-ary linear codes from one-Lee weight codes over IFp+ v IFp, which attain the Plotkin bound and the Griesmer bound. The authors also obtain a class of optimal p-ary linear codes from two-Lee weight projective codes over IFp + vIFp, which meet the Griesmer bound.     

4维3元近链线性码的重量谱

GF（q）上[n,k;q]线性码C的重量谱为序列（$d_1,d_2,\cdots,d_k$），这里$d_r$是C的r维子码的最小支持重量。文章利用射影几何方法确定了满足近链条件的4维3元码的所有重量谱。     

Study on cipher propertys of constant weight codes

1 .INTRODUCTIONIn the research on constant weight codes , someconsiderable headway have been made in the do-main of the binary constant weight codes . Espe-cially ,people focus attention on the functionA(n,d, w) ,which denotes the maxi mumcardinality ofa binary code of lengthn,mini mumdistancedandconstant weightw.Some newresults on upper andlower bounds onA( n, d, w)are presented inRefs .[1 ~4] ,and the result on extensive constantweight codes is givenin Refs .[5 ~10] ,respective-ly .In …     

Construction of one-Lee weight and two-Lee weight codes over F<Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> + <Emphasis Type="Italic">v</Emphasis>F<Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over F _p + vF _p (v ² = v) with type \({p^{2{k_1}}}{p^{{k_2}}}{p^{{k_3}}}\) based on two different distance-preserving Gray maps from ((F _p + vF _p ) ⁿ , Lee weight) to (F _p ²ⁿ , Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p = 2.     

A MacWilliams type identity on Lee weight for linear codes over \mathbb{F}_2 + u\mathbb{F}_2^*

In this paper,the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F₂ + uF₂ is determined.As an application of this identity,the authors obtain a MacWilliams type identity on Lee weight for linear codes over F_2^m+ uF_2^m.Furthermore,the authors prove a duality for the m-ply Lee weight distributions by taking advantage of the Krawtchouk polynomials.     

On LCD Negacyclic Codes over Finite Fields

This paper deduces the structure of LCD negacyclic codes over the finite field Fq, where q is an odd prime power. Based on the study of q-cyclotomic cosets modulo 2 n, the authors obtain the parameters of LCD negacyclic codes of lengths n =(q+1)/2,(q~m-1)/2(q-1)and q~(t·2~τ)-1/2(q~t +1), respectively. And many optimal codes are given. Moreover, the authors research two special classes of MDS LCD negacyclic codes of length n |(q-1)/2 and n |(q+1)2, respectively.     

3维与4维q元线性码的重量谱

得到了不满足链条件的 [n,3;q]线性码 ( q =8,9)的差序列的充要条件 ;并应用改进的遗传算法搜索满足链条件的 [n,4 ;4 ]线性码的差序列 ,取得了较好的结果 .     

ON THE SECOND GREEDY WEIGHT FOR LINEARCODES SATISFYING THE FULLRANK CONDITION

The maximum of g2-d2 for linear [n, k, d; q] codes C is studied. Here d2 is the smallest size of the support of 2-dimensional subcodes of C and g2 is the smallest size of the support of 2-dimensional subcodes of C which contains a codeword of weight d. The extra cost to the greedy adversary to get two symbols of information using some algorithm is g2-d2. For codes satisfying the fullrank condition of general dimensions, upper bounds on the maximum of g2-d2 are given. Under some condition we have got code C where g2-d2 reaches the upper bound.     

A DECODING ALGORITHM FOR GENERAL ZZ4-LINEAR CODES

In this correspondence, a decoding algorithm for the general ZZ_4-linear codesis given and the complexity of the decoding algorithm is estimated.     

几种跳频码的混沌动力学特性及预测分析

利用动力系统方法研究了几种跳频码(m序列，RS序列，非线性序列及混沌序列)的动力学特性(相关维数与最大李雅普诺夫指数)，结果表明了跳频码表现出混沌的特征。最后根据遗传算法确定前馈神经网络的结构，并利用该神经网络模型对这几种序列做了预测分析。实验结果表明，该模型能成功地预测跳频码，因而可对跳频通信进行有效的干扰。     

A NEIGHBORHOOD UNION CONDITION FOR PANCYCLIC GRAPHS

1.IntroductionWeconsideronlysimplefinitegraphs.OurbasicnotationandterminologynotdefinedherefollowthOSeofBondyandMurtyll].ForagraphG,letV(G)andE(G)(orjustVandE)deDOtelievertexsetandedgeset,respectively.Wedenoteapathandacyclecontaining8veniCesbyPaandCarespectively.ThecycleCaiscalledans-cycle.Denotebyg(G)(orbrieflybyg)thegirthofG1.SetNC=min{IN(u)UN(v)l:tv相似文献   

CONSTRUCTIONS OF THREE-TRANSMIT-ANTENNA SPACE-TIME CODES

In this paper, we give design methods for three-transmit-antenna space-time codes which have reasonable parameters. A few examples are given to show that some unitary space-time codes constructed with our methods are better than the previously best-known ones.     

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

This paper considers the Rosenau equation with a moving control?t u + ?_t?_x~4 u + ?_xu + u?x u = a(x + ct)h(x, t), c = 0, x ∈ T = R/(2πZ), t 0.The authors prove that the Rosenau equation with a moving control is locally exact controllable in Hs(T) with s ≥ 0 and globally exponential stable in H~s(T) with s ≥ 2. The two results nontrivially extend the work of(Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.     

LDPC码偏移修正加权比特翻转译码算法

大量仿真表明,基于幅度和的改进型加权比特翻转(modified sum of the magnitude based weighted bit flipping, MSMWBF)译码算法对于行重/列重较小的低密度奇偶校验(low density parity check, LDPC)码而言,展现出巨大的性能优势,但对于行重/列重较大的基于有限域几何(finite geometry, FG)的LDPC码,性能损失严重。首先对此现象进行理论分析。其次,引入附加的偏移项对MSMWBF算法的校验方程可靠度信息进行修正,提高了算法对行重/列重较大的LDPC码的译码性能。仿真结果表明,在加性高斯白噪声信道下,误比特率为10E-5时,相比于MSMWBF算法,在适度增加实现复杂度的条件下,所提算法可获得约0.63 dB的增益。     

基于相对残差的LDPC码动态调度译码算法

针对低密度奇偶校验码的动态调度译码算法中存在的震荡现象和贪婪特性问题,在基于变量节点消息残差置信传播算法的基础上,提出一种基于相对残差调度的置信传播算法。对变量节点进行分组,以变量节点向校验节点传递消息的相对残差值作为参考,优先更新相对残差值最大的节点,加快译码收敛速度。对于译码过程中震荡的变量节点,对其更新前后的后验LLR(log likelihood ratio)消息值做加权平均处理,提高震荡节点的可靠度。在算法迭代的过程中对变量节点向校验节点传递消息的相对残差值作衰减处理,缓解译码算法的贪婪特性。仿真结果表明：与VC-RBP算法相比,在误比特率为10-5时所提算法译码性能可以获得0.3～0.4 dB的增益,同时拥有更快的收敛速度。     

软判决在纠错编码中的应用

纠错编码中解调后对输出信息不判决而直接送给译码器进行译码的方法称为软判决方法,这样得到的信息就是软信息.从信息论的角度分析了软判决和硬判决时的信道容量,通过数学推导得到两种判决方式下信道容量的表达式,简要介绍了卷积码和Turbo码的编译码方法,并将软判决的观点应用于卷积码和Turbo码中.仿真结果表明,在解调器的输出端使用软判决的方法对这两种纠错编码方式来说都可以得到2dB左右的编码增益.